Results 1 
5 of
5
Coherence for sharing proofnets
 Proceedings of the 7th International Conference on Rewriting Techniques and Applications (RTA96), LNCS 1103
, 1996
"... Sharing graphs are an implementation of linear logic proofnets in such a way that their reduction never duplicate a redex. In their usual formulations, proofnets present a problem of coherence: if the proofnet N reduces by standard cutelimination to N 0, then, by reducing the sharing graph of N ..."
Abstract

Cited by 11 (7 self)
 Add to MetaCart
(Show Context)
Sharing graphs are an implementation of linear logic proofnets in such a way that their reduction never duplicate a redex. In their usual formulations, proofnets present a problem of coherence: if the proofnet N reduces by standard cutelimination to N 0, then, by reducing the sharing graph of N we donot obtain the sharing graph of N 0.Wesolve this problem by changing the way the information is coded into sharing graphs and introducing a new reduction rule (absorption). The rewriting system is con uent and terminating. The proof of this fact exploits an algebraic semantics for sharing graphs. 1
Proof nets, Garbage, and Computations
, 1997
"... We study the problem of local and asynchronous computation in the context of multiplicative exponential linear logic (MELL) proof nets. The main novelty isin a complete set of rewriting rules for cutelimination in presence of weakening (which requires garbage collection). The proposed reduction s ..."
Abstract

Cited by 7 (6 self)
 Add to MetaCart
We study the problem of local and asynchronous computation in the context of multiplicative exponential linear logic (MELL) proof nets. The main novelty isin a complete set of rewriting rules for cutelimination in presence of weakening (which requires garbage collection). The proposed reduction system is strongly normalizing and confluent.
Resource operators for λcalculus
 INFORM. AND COMPUT
, 2007
"... We present a simple term calculus with an explicit control of erasure and duplication of substitutions, enjoying a sound and complete correspondence with the intuitionistic fragment of Linear Logic’s proofnets. We show the operational behaviour of the calculus and some of its fundamental properties ..."
Abstract

Cited by 6 (3 self)
 Add to MetaCart
We present a simple term calculus with an explicit control of erasure and duplication of substitutions, enjoying a sound and complete correspondence with the intuitionistic fragment of Linear Logic’s proofnets. We show the operational behaviour of the calculus and some of its fundamental properties such as confluence, preservation of strong normalisation, strong normalisation of simplytyped terms, step by step simulation of βreduction and full composition.
Proof Nets and the λcalculus
 Linear Logic in Computer Science, 65–118
, 2004
"... In this survey we shall present the main results on proof nets for the Multiplicative and Exponential fragment of Linear Logic (MELL) and discuss their connections with λcalculus. The survey ends with a short introduction to sharing reduction. The part on proof nets and on the encoding of λterms ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
(Show Context)
In this survey we shall present the main results on proof nets for the Multiplicative and Exponential fragment of Linear Logic (MELL) and discuss their connections with λcalculus. The survey ends with a short introduction to sharing reduction. The part on proof nets and on the encoding of λterms is selfcontained and the proofs of the main theorems are given in full details. Therefore, the survey can be also used as a tutorial on that topics. 1
Sharing Implementations of Graph Rewriting Systems
 TERMGRAPH ’04 PRELIMINARY VERSION
, 2004
"... Sharing graphs are a brilliant solution to the implementation of Lévy optimal reductions of λcalculus. Sharing graphs are interesting on their own and optimal sharing reductions are just a particular reduction strategy of a more general sharing reduction system. The paper is a gentle introduction t ..."
Abstract
 Add to MetaCart
Sharing graphs are a brilliant solution to the implementation of Lévy optimal reductions of λcalculus. Sharing graphs are interesting on their own and optimal sharing reductions are just a particular reduction strategy of a more general sharing reduction system. The paper is a gentle introduction to sharing graphs and tries to confute some of the common myths on the difficulty of sharing implementations.